g-2 Eigo Shintani (RIKEN-CCS) with Yoshinobu Kuramashi (Tsukuba) - - PowerPoint PPT Presentation

Analysis of systematic error in hadronic vacuum polarization contribution to muon g-2

Eigo Shintani (RIKEN-CCS)

with Yoshinobu Kuramashi (Tsukuba) and PACS collaboration LATTICE2018, 22-28 July 2018, Kellogg Hotel and Conference Center

Contents

1.

Introduction & background

2.

Setup

3.

Finite volume study

4.

Lattice artifact study

5.

Summary

2

 HVP contribution to muon g-2

• 1. Introduction & background

Motivation

3

Target precision is < 1% in LQCD Dispersion approach(Nf=5) using R-ratio (e+e-) : am

HLO = 688.6(4.3) × 10-10 ⇒ 0.6 % precision

Jegerlehner, 1511.04473

Err[am

BNL] = 6.3×10-10

Will be factor 5 improvement in the new experiment in FNAL, JPARC

QCD uncertainty is comparable with BNL experimental uncertainty. Independent check in LQCD is important. Need to improve the precision to ~0.5% of HVP muon g-2 in the SM. ⇒ search the new physics in muon g-2 anomaly (~3 σ deviation)

 Time-momentum rep. (TMR) method

• 1. Introduction & background

g-2 with time-slice integral

• Vector current correlator <VV>(t) without momentum.

Bernecker, Meyer, EPL A47(2011)

4

• FV effect and tcut truncation error.
• Large statistical noise in long distance.
• Lattice artifact in short time-slice.

Possible uncertainties in both long and short distances

5

 FV effect

 Using the new PACS configs., which are large box size L >10 fm,

in the physical pion.

 T

wo volumes at same cut-off ⇒ direct estimate of FV effect

 Statistical noise

 Optimized AMA technique in Wilson-clover  Volume scaling of S/N ⇒ large volume can reduce noise

 Lattice artifact

 Comparison with different cut-off.  T

est of operator dependence

• 1. Introduction & background

Our strategy

Mainz, NPB914 (2017)

Here we calculate connected HVP contribution only.

6

 Previous study on 964 and 644 lattice

• 2. Setup

Update

PACS 1805.04250

• Attempt LQCD estimate of

FV.

• 964 lattice:145 MeV pion

644 lattice:135 MeV pion ⇒ chiral extrapolation

• am[L=8.1fm] - am[L=5.4fm]

= (10±26) in 145 MeV

• LQCD does not disagree

with ChPT, but statistical error is still large.

New PACS ensemble, which is L>10 fm in 135 MeV pion. ⇒ direct estimate of FV

7

 Iwasaki gauge + stout smeared clover fermion  Physical pion mass in Nf = 2+1  Old configuration

 644, a-1=2.33 GeV, mp=139 MeV and 135 MeV(reweighted)

 New configuration generation (PACS10)

 1284, a-1=2.33 GeV, mp=135 MeV  1604, a-1=3.06 GeV, mp=135 MeV

• 2. Setup

PACS10 configuration

PACS, 1807.06237

Using PACS10 configs., we can study

• Direct estimate of FV effect on L=5.4 fm in mp =135 MeV
• Cut-off effect on L>10 fm box in mp =135 MeV

All data is still preliminary !

• 2. Setup

Effective mass

8

• In t > 1 fm, effective mass of

vector channel is below rho meson mass.

• Epp

free < mv < mr

• 2. Setup

Volume scaling of stat. error

9

• Volume scaling of statistical error

in long-distance, t > 1.5 fm

• Volume scaling is universal in

different cut-off. ⇒ depending on physical volume

• 3. Finite volume study

Comparison with 1284 and 644

10

Integrand, T/a=64 Integrand, T/a=128, extended t

• Backward propagation state significantly affects in T/a=64 from t~2 fm(~T/2)

⇒ check with extended temporal boundary

• LQCD estimate of FV correction is larger than ChPT at t>1.5 fm

PACS 1805.04250

mp=139 MeV mp=135 MeV (valence) mp=135 MeV (reweighted)

• 3. Finite volume study

FV effect in L=5.4 fm

11

T

• sum, T/a=128, extended t

mp=139 MeV mp=135 MeV (valence) mp=135 MeV (reweighted)

LQCD (tcut = 3fm): am[L=10.8fm] - am[L=5.4fm] = 40(18), ChPT: 14 ⇒ ~2.5x underestimate

Mass correction (4 MeV) agrees with ChPT.

PACS 1805.04250

• 3. Finite volume study

FV in Strange

12

FV in strange is negligibly small. ⇒ light quark contribution is dominant

• 4. Lattice artifact study

Comparison with a-1=2.33 and 3.06 GeV

13

• Comparison between local-

local and local- conserved(point-splitting) current.

• Local-local has good scaling

rather than local-conserved

• ne at t ~ 1 fm.

• 4. Lattice artifact study

Comparison with a-1=2.33 and 3.06 GeV

14

• Small scaling violation in local-local current even without improvement.
• In local-conserved current, one can see 4—5 % cut-off effect in ud and s.

• 4. Lattice artifact study

LQCD and phenomenology

15

• Compared to R-ratio,

LQCD has large value at t < 3fm.

• From t ~ 3fm, R-ratio

is relatively large, whose integral from t=3--∞ gives ~3% contribution in total am.

• 4. Lattice artifact study

am in LQCD and phenomenology

16

• tcut>2.5 fm, we can see

LQCD overshoot phenomenological estimate.

• tcut > 3 fm, LQCD is

saturated around am

Exp – am QED+EW+LbL

(“no new physics”)

• 4. Lattice artifact study

Cut-off effect in am

17

• Estimate at tcut = 3.5 fm,

which may be ~1% truncation error.

• Scaling violation is not
• bserved in local-local

current beyond statistical error.

• LQCD will not favor

phenomenological value.

• Continuum limit is

mandatory, but not yet.

 Updated result of FV study in LQCD.  FV study at physical pion

 At tcut = 3fm, LQCD estimate is ~2.5x larger than ChPT.  Possible impact to other LQCD estimate of FV based on ChPT.

 Lattice artifact study

 Compared to two different cut-off  Scaling violation is small even in local-local current on PACS10,

while local-conserved has large effect (4—5 %).

 Next work

 am

ud + am s in LQCD is close to am Exp – am QED+EW+LbL

 Missing am

c + am disc, but may be <1%, since |am c| ~ -|am disc| ~ 1%

 Continuum limit is necessary for final result, need one more cut-off.

• 4. Summary

Outlook

18

PACS 1805.04250

(“no new physics”)

Backup

19

Backup

Operator dependence

20